Wow. This has been a great day for difficult questions! Thanks for making me blow the cobwebs out of this dusty brain!
Okay, let's dive right in. I am going to guess that you are referring to the phrase "Tat Tvam Asi," the Sanskrit phrase that roughly translates as either "That art thou," "You are that," or "That you are" depending on who you ask. Those are the translations people are pretty sure of. Unfortunately, that's about all people are sure of when it comes to this phrase.
Interpreting it depends a lot on your point of view, and in this case it depends on how you are interpreting certain Hindu religious texts. The one that I like best, and that makes the most sense (especially to Western readers,) is the one that comes from the Advaita Vedanta (the dominant school of thought for the interpretation of Hinduism.)
Essentially, what the phrase is saying (at least according to the Advaita school of thought) is that the phrase means that there is no separation of people from Brahman (God.) The phrasing is hard to get around and would even if it wasn't so old. It takes a good deal of poking and prodding to make sense of it, so I won't even try.
Tat Tvam Asi is essentially saying that Brahman (the creator of reality and everything else,) though veiled by Maya (the illusion that the world around us is real,) is the same as what we might call "our spirit" (in a Christian sense.) The idea is that the real stuff people are made of is the same that makes up God (Brahman.)
That Thou Art (Tat Tvam Asi). The direct meaning of the word 'THAT' comprises the conditioned Brahman (associated with the limited adjuncts of creation, preservation and destruction and endowed with Omniscience, Lordship, Omnipotence and similar attributes) and Pure Consciousness which is its unrelated substratum.
Likewise the direct meaning of the word 'THOU' comprises the jiva or individual soul (associated with the limiting adjuncts of the body, mind and the sense organs and endowed with such traits as little knowledge, little power, and dependence), and Pure Consciousness which is its unrelated substratum.
But there is also an implied meaning of the words 'THAT' and 'THOU', namely Pure Consciousness itself, unassociated with any limiting adjuncts. It is common practice to explain a statement through its implied meaning when the direct meaning contradicts actual experience: when we say that a red hot iron ball burns something, we say the direct agent of burning is the iron; but the implied though real agent is fire, unassociated with iron.
Again in the statement "He spent the night on a sleepless pillow", the word 'sleepless' does not refer to the pillow but to the person who used the pillow. Similarly in the Vedic statement 'THAT THOU ART' the word "ART" denoted the identity of 'THAT' and "THOU", which directly refers to the conditioned Brahman and the embodied soul respectively. But this identity is obviously absurd, since they are poles asunder. Therefore, we must explain the statement by its implied meaning.
The identity is really based upon the Pure Consciousness which is the unrelated substratum of both. The limiting adjuncts in both cases are the creation of ignorance and therefore unreal; so these must be discarded.
Therefore the statement "THAT THOU ART" really conveys a
transcendental experience of oneness which is beyond the body, mind, senses and ego and the sensations associated with them. When a person realises this oneness with Brahman. he is oblivious of the idea that he is an embodied being.